Francis Bitter Magnet Laboratory, and Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
J Chem Phys. 2011 Mar 28;134(12):125105. doi: 10.1063/1.3564920.
Microwave driven dynamic nuclear polarization (DNP) is a process in which the large polarization present in an electron spin reservoir is transferred to nuclei, thereby enhancing NMR signal intensities. In solid dielectrics there are three mechanisms that mediate this transfer--the solid effect (SE), the cross effect (CE), and thermal mixing (TM). Historically these mechanisms have been discussed theoretically using thermodynamic parameters and average spin interactions. However, the SE and the CE can also be modeled quantum mechanically with a system consisting of a small number of spins and the results provide a foundation for the calculations involving TM. In the case of the SE, a single electron-nuclear spin pair is sufficient to explain the polarization mechanism, while the CE requires participation of two electrons and a nuclear spin, and can be used to understand the improved DNP enhancements observed using biradical polarizing agents. Calculations establish the relations among the electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) frequencies and the microwave irradiation frequency that must be satisfied for polarization transfer via the SE or the CE. In particular, if δ, Δ < ω(0I), where δ and Δ are the homogeneous linewidth and inhomogeneous breadth of the EPR spectrum, respectively, we verify that the SE occurs when ω(M) = ω(0S) ± ω(0I), where ω(M), ω(0S) and ω(0I) are, respectively, the microwave, and the EPR and NMR frequencies. Alternatively, when Δ > ω(0I) > δ, the CE dominates the polarization transfer. This two-electron process is optimized when ω(0S(1))-ω(0S(2)) = ω(0I) and ω(M)~ω(0S(1)) or ω(0S(2)), where ω(0S(1)) and ω(0S(2)) are the EPR Larmor frequencies of the two electrons. Using these matching conditions, we calculate the evolution of the density operator from electron Zeeman order to nuclear Zeeman order for both the SE and the CE. The results provide insights into the influence of the microwave irradiation field, the external magnetic field, and the electron-electron and electron-nuclear interactions on DNP enhancements.
微波驱动的动态核极化（DNP）是一种将电子自旋库中存在的大极化转移到核上，从而增强 NMR 信号强度的过程。在固体电介质中，有三种机制介导这种转移——固体效应（SE）、交叉效应（CE）和热混合（TM）。历史上，这些机制一直使用热力学参数和平均自旋相互作用进行理论讨论。然而，SE 和 CE 也可以使用由少量自旋组成的系统进行量子力学建模，结果为 TM 的计算提供了基础。在 SE 的情况下，单个电子-核自旋对足以解释极化机制，而 CE 需要两个电子和一个核自旋的参与，并可用于理解使用双自由基极化剂观察到的增强 DNP。计算建立了电子顺磁共振（EPR）和核磁共振（NMR）频率与微波辐照频率之间的关系，这些关系必须满足通过 SE 或 CE 进行极化转移的要求。特别是，如果 δ、Δ < ω(0I)，其中 δ 和 Δ 分别是 EPR 谱的均匀线宽和非均匀宽度，我们验证了当 ω(M) = ω(0S) ± ω(0I)时，SE 发生，其中 ω(M)、ω(0S) 和 ω(0I) 分别是微波、EPR 和 NMR 频率。或者，当 Δ > ω(0I) > δ 时，CE 主导极化转移。当 ω(0S(1))-ω(0S(2)) = ω(0I) 且 ω(M)~ω(0S(1)) 或 ω(0S(2)) 时，这个双电子过程得到优化，其中 ω(0S(1)) 和 ω(0S(2)) 是两个电子的 EPR 拉莫尔频率。使用这些匹配条件，我们为 SE 和 CE 计算了从电子塞曼顺序到核塞曼顺序的密度算符的演化。结果提供了对微波辐照场、外磁场以及电子-电子和电子-核相互作用对 DNP 增强的影响的深入了解。
